Anharmonic Effect on Heat Capacity of Solids up to the Critical Temperature of Lattice Instability

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Abstract
Anharmonic contribution to the thermal energy is evaluated for solids at temperatures higher than Debye temperature, with the assumption that anharmonic effects are expressed by the pseudoshift in the angular frequency of normal mode. Here the angular frequencies are assumed to depend on the mean thermal energy as well as on the volume. Both the thermal and caloric equations of state are derived systematically from the same partition function of this extended quasiharmonic treatment. Heat capacity is calculated as a function of temperature on the basis that the frequency shift occurs through the "vibrational elongation" introduced by Ida in the theory of lattice instability. The calculation describes a qualitatively correct curve of heat capacity. It is again shown that the lattice will be unstable above a critical temperature because of anharmonicity.